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Hello!
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This is a brief bonus lecture
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and what I'm gonna do in this lecture
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is show you that there're infinite number
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of prime numbers.
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In other words,
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I'm gonna prove the infinitude of primes.
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Now, this is really one of the gems
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of the history of mathematics
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and the history of science,
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and using, as we'll see in a moment,
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just primitive tools for the most part
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we can prove that, in fact,
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there're infinite number
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of prime numbers.
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And, as I've indicated,
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this proof goes back
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to someone called Euclid,
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who's generally considered
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the founder (one of the founders)
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of geometry
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and the proof dates
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to at least 300 BC.
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So let's begin with the definition
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of what a prime number is.
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A prime number
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beginning with then number 2
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is an integer
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greater than or equal to 2
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whose only whole number divisors
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are 1 and itself.
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So, for instance, 2 is the smallest prime.
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3 is the next prime
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in the sequence of primes.
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5 is the next.
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7, 11, 13, and so forth.
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